functor

(redirected from Cofunctor)
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functor

[′fəŋk·tər]
(computer science)
(mathematics)
A function between categories which associates objects with objects and morphisms with morphisms.

functor

In category theory, a functor F is an operator on types. F is also considered to be a polymorphic operator on functions with the type

F : (a -> b) -> (F a -> F b).

Functors are a generalisation of the function "map". The type operator in this case takes a type T and returns type "list of T". The map function takes a function and applies it to each element of a list.
References in periodicals archive ?
We recall Weiss' construction of polynomial cofunctors as suitable extensions of cofunctors defined only on [O.
12) that any valid choice (as described above) of special open sets yields equivalent notions of polynomial cofunctors and polynomial approximation by polynomial cofunctors.
4 in [8] shows that the cofunctors Emb(-, N) and Imm(-, N) are good, where Emb and Imm denote the spaces of smooth embeddings and immersions, respectively.
Weiss calls these special open sets and shows [8] that k-polynomial cofunctors are determined by their restriction to [O.
If F, G : O [right arrow] Top are polynomial cofunctors of degree [less than or equal to] k, and [gamma] : F [right arrow] G is a natural transformation such that [[gamma].
Namely, we would like to characterize k-polynomial cofunctors by their restriction to some smaller class of special open sets than all of [O.
First, we can very easily strengthen Weiss' characterization of polynomial cofunctors by considering their restriction to [B.
2] be good cofunctors from O [right arrow] Top, both polynomial of degree [less than or equal to] k.
However, the previous characterization of polynomial cofunctors appealed directly to Weiss' result.